Q. 24 - Elementary Statistics

Question

Oxygen Distribution. In the article "Distribution of Oxygen in Surface Sediments from Central Sagami Bay, Japan: In Situ Measurements by Microelectrodes and Planar Optodes" R. Glud et al. explored the distributions of oxygen in surface sediments from central Sagami Bay. The oxygen distribution gives important information on the general bio geo chemistry of marine sediments. Measurements were performed at $16$ sites. A sample of $22$ depths yielded the following data, in millimoles per square meter per day on diffusive oxygen uptake (DOU).
a. Obtain the five-number summary for these data.
b. Identify potential outliers, if any.
c. Construct a boxplot.

Step-by-Step Solution

Answer

Part(a) Five number summary is $0.7, 1.5, 1.95, 3.3, 7.6$

Part(b) Five potential outliers are there.

Part(c) Required graph is given below.

Part(a) Step 1 : Given information

We need to find out the five-number summary

Part(a) Step 2 : Simplify

Five number summary is 

Minimum $=0.7$ 

First quartile $=1.5$ 

Median $=1.95$ 

Third quartile $=3.3$ 

Maximum $=7.6$

Part(b) Step 1 : Given information

We need to find out the potential outliers.

Part(b) Step 2 : Simplify

An outlier is more than $1.5 IQR$ or greater than $Q_3$ or less than $Q_1$

Therefore,

       $$\begin{gathered} Q_3+1.5 IQR= 3.3+\left(1.5\times 1.8\right)=6.0 \\ {Q}_1-1.5 IQR= 1.5+\left(1.5\times 1.8\right)=4.2 \end{gathered}$$

Hence, there is five outlier i.e.  because they does not lie between $6.0$ and $7.8$

Part(c) Step 1 : Given information

We need to find the boxplot which is given below

Part(c) Step 2 : Simplify

The whiskers of the boxplot are at a low and high value. The box starts at $Q_1$ and ends at $Q_3$  and has a straight line at the median.